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UC-NRLF 


B  M  ^^o  t.11 


RICHARD   WiJERST. 

ELEMENTARY  THEORY 
OF  MUSIC. 


^^^^H 

I 

I 


/  %■  ^  k^^U^ 


-<y  y  i^y 


Elementary  Theory 


OF 


MUSIC, 

AND  THE 

TREATMENT  OF  CHORDS, 

BY 

RICHARD  WUERST. 

DIRECTOR  AND  PROFESSOR  OF  MUSIC  AND  MEMBER  OF   THE 
ROYAL  ACADEMY  OF  ARTS,  BERLIN,  PRUSSIA. 


Introduced  for  use  in  the  New  Academy  of  Tone-Art  and  the  Con- 
servatory OF  Music  in  Berlin. 


translated  into  ENGLISH  BY 

MAYNARD     BUTLER. 


FIFTH  EDITION. 


PUBLISHED   BY 

THE   BOSTON    MUSIC   CO., 

BOSTON,   MASS. 

Copyright,  1893,  by  G.  Schirmer,  Jr. 


MT7 


C0 

professor  ^\tatiaxt  lanllah. 


In  dedicating  this  little  work  to  you,  my  dear  friend, 
I  do  so  with  the  double  pleasure  of  presenting  you  with 
a  small  token  of  my  regard  and  admiration,  and  also  as 
an  expression  of  my  appreciation  of  the  fact  that  the  ex- 
perience which  enables  me  to  put  this  book  before  the 
public,  has  been  gained,  for  the  most  part,  in  the  course 
of  the  instruction  given  for  so  many  years,  in  the  Insti- 
tution of  which  you  are  the  Director.  In  this  two-fold 
sense,  I  beg  you  to  accept  it  from 

Yours  faithfully, 

RICHARD  WUERST. 

Berlin^  June  /,  1867. 


TO 
THIS 

tra:nslation  is  dedicated 

WITH   THE 
REMEMBRANCES 

OF  .         * 


^aunartr  §utUr 


BOSTON,  MASS. 


Introduction. 


My  object  in  compiling  this  work,  has  been  to  provide  students 
of  music  with  a  book  as  brief,  practical,  and  yet  complete  as  pos- 
sible, which  should  contain  everything  that  each  one  of  them  ought 
to  learn  and  could  learn. 

I  have,  therefore,  extended  its  limits  only  as  far  as  Modulation 
(  which  is  a  branch  requiring  study  beyond  the  scope  of  the  present 
undertaking  )  and  have  stopped  at  the  point  where  the  material  for 
Chords  and  how  to  deal  with  them,  under  all  circumstances, w4th 
figured  bass,  has  been  made  clear;  for  my  object  has  been  to  write 
a  book  suitable  for  all  students,  not  for  a  favored  few.  There  is 
in  the  work  itself  nothing  new,  but  I  do  believe  that  the  concise 
and,  as  it  seems  to  me,  clear  manner  in  which  its  contents  are  pre- 
sented, are  my  own, and  but  the  natural  result  of  the  experience  of 
fifteen  years  of  teaching  harmony.  I  should  regard  it  as  the  most 
grateful  result  of  my  labor,  if,  by  means  of  it,  the  preparatory  studies 
of  those  who  devote  themselves  to  music  should  be  made  easier, 
their  circle  of  knowledge  enlarged  and  their  interest  in  it  increased; 
and  that  of  these,  they  who  possess  talent,  might  acquire  through 
it,  a  more  thorough  foundation  of  the  theory  of  their  art,  than,  alas  ! 
they  too  frequently  possess. 

RICHARD    WUERST. 


CONTENTS. 


Alia  breve .        .        .        .         -14 

Alto  Clef 10 

Appendix 49 

Augmented  Triad 25 

Bass 

Bis  .        .        .        . 15 

Brevis .12 

O  Clefs . 10 

Chords  .        . 24 

Chord  of  the  Dominant  7th  =7 34 

Chord  of  the^Second     . -36 

Chord  Position .25 

Chromatic  Scale 25 

Concealed  False  Progressions .28 

Combining  of  Chords 

Contra  Octave -9 

Cross  Position .28 

I>a  Capo 15 

Deceptive  Cadences      . .         ,         .         .         .46 

Diatonic  Major  Scale 20 

Diminished  Triad 

Discant  or  Soprano  Clef       .         .         . 10 

Division  of  the  Minor  Coloring  in  Music .22 

Divisions  of  Tone-Coloring  in  Music    .,...<... 

Double  Dot 13 

Double  Triplet 13 

Doubling  of  Intervals 25 

Dynamic  Signs ^ 19 

Elementary  Theory 9 

Enharmonic .         .20 

Enharmonic  Table '.         .         .         .20 

Exceptions  to  the  Rule  against  False  Progressions 28 

False  Progressions -27 

Fermate .         •     ^5 

Fourths .- 24 

Half-Tones 19 

Harmonic  Minor  Scale 22 

(7) 


Intervals 24 

Inversion -      .         .29 

Irregular  resolution  of  the  Dominant  Seventh  Chord 36 

Kleys 21 

Kinds  of  Time 14 

Leading  Note 23 

Miajor  Triad 24 

Melodic  Minor  Scale    .         .         .         .         .         .         .         .         .        .         .         .22 

Minor  Tone-Coloring ,         .        .        .         .22 

Minor  Triad .,...,     24 

Mixed  Chords  of  the  Seventh       .         .         .         .         ...         .         .         -43 

JVames  of  Tones  . 9 

Notes 12 

Other  Chords  of  the  Seventh 47 

Parallel  Keys 22 

Pauses  or  Rests 12 

R/epetition  Signs 15 

Rests 

Rhythm 12 

Seconds .24 

Signature 21 

Soprano  Clef 10 

Syncoi^ation  .         .         .         .         .         .         .         .         .         .         .         .         ,         -IS 

Table  of  Chords           .         • .  42 

Table  of  Intervals  of  the  Eight  Chords  of  the  Seventh 45 

Table  of  Kinds  of  Measure  .         .         .         .         .         .         .         .         .  *      .         .16 

Table  of  Major  Scale ; 20 

Table  of  Clefs        ......". 11 

Tempo 18 

Tempo  Signs 18 

The  Chord  of  the  Fifth  and  Fourth  =  |  Chord          . ' 33 

The  Chord  of  the  Second,  Sixth  and  Seventh  —  e  Chord  .         .         .         -39 

The  Chord  of  the  Sixth  =  6  Chord .         .     ,    .  29 

The  Chord  of  the  Sixth  and  Fifth  -=  ^  Chord 35 

The  Chord  of  the  vSixth  and  Fourth  =  £  Chord 32 

The  Chord  of  the  Third  and  Fourth  =  I  Chord 35 

The  Circle  of  Fifths 22 

The  Clef 9 

The  Five  Clefs      .        .        .        .  ,     .        . ' 9 

The  Lower  Dominant   .         .         ...         .        . 23 

The  Lower  Mediant 23 

The  Octave 24 

The  Scale 20 

The  Sextolet 13 

The  Staff 9 

The  Tenth 24 

The  Tie 15 

The  Tonic 23 

The  Triad 24 

The  Triplet 13 

Thorough  Kass .25 

Time 14 

Tone,  Whole  Tone,  Half  Tone 9,  19,  19 

Tone-System 9 


ELEMENTARY  THEORY. 


A  Musical  Tone  is  a  Sound  oi  Jixed  height  or  depth :  the  collec- 
tion of  musical  tones  is  called  the  Musical  System :  this  System  is 
designated  by  seven  names ; 

English  — C,  D,  E,  F,  G,  A,  B. 
German— C,  D,  E,  F,  G,  A,  H. 
French  — Ut,  Re,  Mi,  Fa,  Sol,  La,  Si. 
Italian  —  Do,  Re,  Mi,  Fa,  Sol,  La,  Si. 

These  sev^en  names  naturally  recur  again  and  again,  and  upon  the 
repetition  of  the  first,  which  is  then  called  the  Eighth^  the  scope 
which  they  embrace  is  termed  an  Octave. 

The  lowest  octave  which  receives,  in  technical  language,  an 
especial  name,  is  the  Contra  Octave;  then  follow  the  Greater 
Octave^  the  Lesser  Octave^  the  First,  Second,  Third-lined,  etc.* 

The  two  divisions  into  which  Xone  Color  in  music  is  separated 
are  Major  and  Minor;  in  German,  Dur  and  MolL 

The  Musical  6^/(7^  consists  of  five  Lines^  the  lowest  of  which  is 
called  \\\Q first',  the  notes  outside  the  Staff  are  indicated  by  means 
of  added  lines^vAi\c\\.  are  to  be  regarded  simply  as  a  continuation 
of  the  staff  itself. 

A  Musical  Clef  is  a  sign  which  specifies  a  certain  place  upon 
the  staff  and  affixes  an  unchangeable  name  to  it ;  there  are  three 
such  clefs: 

The  Violin  or  G  Clef  j^  which  is  placed  upon  the  second  line, 

and  gives  to  that  line  the  name.   One-lined  G. 

The  Bass  or  F  Clef  ^ii  (^ —  which  is  placed  upon  the  fourth 


line,  and  gives  to  that  line,  the  name.  Lesser  F, 

*  In  the  absence  of  lines  of  the  staff  the  tones  of  the  Greater  Octave  are  desig- 
nated by  large  letters,  and  those  of  the  Lesser  by  small  ones ;  as  C,  the  Greater 

Octave  ;    c,  the  Lesser ;   c  the  first-lined ;  etc 

9 


—  10  — 

The  C  Clef  which  gives  to  the  line  upon  which  it  is  placed  the 
name,  One-lined  or  Middle  C. 
This  is  divided  into  three  kinds : 


a.     The  Discant  or  Soprano  Clef  upon  the ^r^/  line  ; 


^ 


b.     The  Alto  Clef  upon  the  third  line  ;   cjj^ 


c.     The  Tenor  Clef  upon  the  fourth  line;* 


A  table  of  these  five  Clefs  would  be  thus  represented : 

*  It  was  the  custom,  formerly,  to  divide  the  Violin  Clef  into  Violin  and  High 
Violin  Clefs,  the  latter  being  written  upon  the  Jirsl  line.  The  Bass  Clef  was  written 
for  Baritone  upon  the  third  C  clef,  for  Mezzo-Soprano^  upon  the  second  line.     The 

sign  for  the  C  clef  was  also  made  thus : —  ilS   or  ifS 


—  11 


n 

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rrr' 
7 

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^ 

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g    CL^lIM 

CO 

o 

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2 

5 

o    ^•1111 

2.    H^  41  11 

^    CfQ     '•111 

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^    P     411 

^     •il 

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9         ^4!| 

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H 

P 

P                  P          1* 

Pti 

d; 

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Z 
o 

H- 

p              P 

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p    < 

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P         *         ' 

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CD 

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cr 

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inii!» 

—  12  — 

Rhythm  has  a  two-fold  significance  in  music :  it  refers  both  to 
duration  of  time  and  to  stress:  the  first,relates  to  Notes  and  their 
equivalent  Rests ;  the  second,  to  Measure, 

Notes*  are  divided  into : 
Whole 

Half 


r 


Quarter 

'^  t  ^  '^ 

Eighths 

p  W  P  P  ^  P  P 

'>  "^  ^  ^  '  '  ' 


5    «    «    f 


Sixteenths 

k*  b  b  i 

Thirty-seconds 


Sixty-fourths 

p§pp»p»^pppppppp^ppp 

^'iiffii    etc. 

Notes  to  be  w^ritten  above  the  third  line  on  the  staff,  are  turned 
down^  tow^ard  the  left;  those  below  the  third  line  are  turned  uf^ 
toward  the  right ;  those  07i  the  third  line  may  be  turned  down  or 
up,  according  to  convenience. 

For  Example  : 

A ^ P- — :   i   :   i   I   I— , 


In  cases  like  that  of  the  six  sixteenths  the  majority  of  the  notes 
govern  the  direction  in  which  the  stems  of  all  are  to  be  written — 
upward  or  downward. 


Rests  are  divided  into  the  Whole  Rest  —  which  hangs  from  a 
a  line  and  fills  one-half  of  a  space. 

*  Formerly,other  notes  were  in  use  than  those  adopted  to-day.  One  of  these  — 
the  Brevis  ^^  ,  which  has  the  value  of  eight  quarter  notes — is,  in  rare  instances, 
still  to  be  met. 


—  13 


The  Half  Rest  _-_    which    lies  upon  the  line  and  fills  one-half 

of  a  space. 

Quarter  Rest  >^  or  less  frequently  ^. 
Eighth  Rest  i. 
Sixteenth  Rest  3. 
Thirty-Second  Rest  3. 

Sixty-Fourth  Rest  q. 

The  Double   Whole  Rest  ~J~  which  fills  a  whole  space. 

The  Four-Measure  Rest  nln  which  fills  two  spaces. 

If  a  number  of  measures  is  to  be  held,  their  equivalents; are  to 

7      

be  combined  out  of  the  rests  just  indicated,  as  —-i      1— —      or  two 

heavy  diagonal   lines  are  written  across   a  single   measure,  above 
which  the  desired  number  of  measures  to  be  silent,  is  indicated  by 

132 
numerals,  as — ^5— 


The  Dot  lengthens  the  note  or  the  rest  after  which  it  is  placed, 
half  of  its  value  :        I    =  | 

The  Double  Dot  lengthens  the  first  dot,  one-half  of  its  value : 

I         _    1         i         _    _7_* 
^  .  .  —    8       ^  .  .  —    16 

The  Triplet  arises  from  the  division  of  a  single  note  or  rest 

into  three  parts ;   these  three  parts  taking  the  value  of  the  note  or 

rest  next  in  order  below  the  given  note  or  rest.     For  example : 
3  3 

I  =    I      I      I  1=1        I        I 

4        4     d     d  g^        4      4      4 

A  group  of  six  notes  of  equal  value,  of  w^hich  the  first  and  the 

fourth    are    accented    is     called    a    double   triplet ;     for    example, 

3 3 

J  ^  ^  J  ^  J;   if    however    the  frst^    the    third  and  the  fifth  are 


accented,  the  group  is  called  a  sextolet.     For  example  :   I J  J  i  m 


*  Every  successive  dot  lengthens  the  preceding  one  half  of  its  value  ;  more  than 
two  dots,  however,  very  rarely  occur. 


—  14  — 

Time,  in  music,  is  Equality  of  Accent. 

Strictly  speaking  there  are  but  two  kinds  of  Time ;  Two-part 
time  and  Three-part  time,  but  for  the  sake  of  convenience  these  are 
divided  into  Simple  two-part  time  and  Compound  two-part  time, 
and  Simple  three-part  time  and  Compound  three-part  time. 

*  Simple  two-part  time  includes,  {^^  g,  |,  2^  g^ 

Compound  two-part  time  includes,  4,  §,  ^j^. 

Simple  three-part  time  includes,  3^  3^  |. 

Compound  three-part  time  includes,   9,  |. 

Table  of  Kinds  of  Time. 


Two-Part: 
Simple;  g,  ^,  |,  2,  |. 

Compound  :   ^,  ^. 

Three-Part: 
Simple  :   |,  3,  3_ 


In  beating  time,  in  directing, 

o 

two  beats  take  the  fol- 
lowing motion :  0 

Three  beats  :    2  ^    1         4 


Compound:   %.%.  9^— i— ^3 

I^our  beats  :  \  | 

Compound  |  time  is  derived,  as  the  student  should  notice,  from 
2  time  by  resolving  every  quarter  note  into  a  triplet  of  eighth 
notes :  g  time,  from  2  time  by  resolving  every  half  note  into  a 
triplet  of  quarter  notes :  ^^  time,  from  4  time  by  resolving  every 
quarter  note  into  a  triplet  of  eighth  notes. 

Compound  |  time  is  derived  from  3  time  by  resolving  every 
quarter  note  into  a  triplet  of  eighth  notes :  9  time,  from  3  time  by 
resolving  every  half  notQ  into  a  triplet  of  quarter  notes. f 

Although  £  and  J  time  have  been  used  in  certain  cases,  they  are  so 
unsatisfactory  to  the  innate  feeling  of  rhythm,  that  they  are  not  to  be 
recommended  for  whole  compositions. 

*  If  the  quarter-notes  of  four-four  (|)  time  are  to  be  so  played  as  to  include  two 
at  every  beat,  this  is  called  alia  breve  (  from  the  Italian  "in  short  manner  ")  time, 
and  is  marked  ^.    This  alia  breve  is  the  same  as  |  time. 

t  Of  course,it  follows  that  from  |,  ^,  and  from  |,  ^q  can  be  evolved  ;  but  these 
divisions  rarely  appear. 


—  15 


An  Incomplete  Measure  is  an  unfinished  measure  at  the 
begiiining  of  a  composition,  which  upon  repetition  must  be  com- 
pleted by  its  closing  measure.  ' 

The  Tie  connects  two  notes  lying  upon  the  same  intei-val,   in 
such  a  manner  as  to  make  them  sound  but  as  one  note. 
-     The  Syncope  connects  notes  lying  upon  the  same  interval  in 
such   a  manner   as  to    make    them    accented    against   the    natural 
rhythm. 

The  Fermate  or  Pause  ^  indicates  that  the  note  or  rest  over 
which  it  is  placed,  is  to  have  a  longer  duration  than  its  natural 
value  in  the  measure  would  indicate. 

^8 

The    Sign   of    Repetition  t[  or         j    indicates  that  the 

measures  preceding  it,  either  from  the  beginning  of  the  composi- 
tion or  from  a  sign  like  itself,  are  to  be  repeated. 

Repetition  may  also  be  indicated  by  the  words  da  capo — mean- 
ing "  from  the  beginning"  — contracted  D.  C. 

If  one  part  of  the  composition  is  to  be  repeated,  the  Signs  S  or  %. 
may  be  placed  before  it,  and  da  capo^  d'al  Segno^  (contracted, 
D.  C.^D.S.),  meaning  "from  the  Sign"  written  after  it. 

If  the  Repetition  is  to  refer  to  several  measures  only,  a  large 
phrasing  mark  ( slur )  may  enclose  them  and  the  word  bis  — 
*' twice"  —  be  written  above  it. 

Every  measure  has  its  chief  accent  upon  the  first  part  of  the 
measure ;  in  measures  divided  into  two  parts,  the  first  part  has  the 
chief  and  the  second  part  the  secondary  accent ;  in  those  divided 
into  three  parts  the  first  part  has  the  chief  and  the  two  other  parts 
the  secondary  accents. 

In  ^  and  ^2  time,  the  former  being  but  a  combination  of  two  2 
measures  and  the  latter,  of  two  g  measures,  the  third  quarter  in  ^ 
and  the  seventh  eighth  in  ^  2  time,  receive  an  accent.  In  short,  all 
those  parts  of  a  measure  which  are  the  initial  note  of  a  triplet, 
receive  a  slight  accent. 


—  16  — 

The  following  table  shows  the  various  kinds  of  measure  with 
their  different  accents. 


a  ;  4 


S    4 


^ 


4     4    4    4 


J    J 


I        I        I 


m    4     4     0 


4  J 


I    I 


4    4    4    4     4     4 


J   J 


I      ! 


9     a  T  f 

^  J  J  J  J  J  J  J  J  J 


—  17  — 


The  following  example  shows  into  how  many  different   forms 
rhythm  can  be  separated. 


G J J    ^    ^— J J 


-—J 


S. 


'        !    J    J 
1 ^    d    4 


I  I        I 


4    J    J  ;  J 


I     III     I  ,    !! 


C J /TlS J J #_ 


4      ^      ^    #    ^ 


g      I — ?=T=^      I    I — ^      I      I 

H        4       4     4     4        \     4       4        I i_ 


2     j — =*=i — \ — I 

M        4 4     4     4       4 4_ 


4 4 4._m 4_ 


%- 


I       J  I       I  I  I      ^-^  I      3       II 

jO. \      (^      ^      ^ |_,2 i-^S l_i22 1-^2 |_J W 


^     i      rn^    I      I      I      I 

^       4-      4     4     4     4'      4- I ^^ 


h J'      4     4     4 


I  I 

4_1 4_ 


fi          I  I      I      I      I       1  I  I 

4 ^J 4     4    4       \     a-      ^'        I     /^ 


I      I 


A^444     ^_^U.J     J.|     J.|l    " 


iJ-JJ 


g  1         I    1      I      I    I     I 

4        cf'      \4     4     4    \a 


I        I     i       I       I      U 
^  -     1-^  •    I    ^  '    I  J- 


Z fi>  .    I  g)    g)    g)     I    ^_^  I    (g  '    I    >g  '    I    ry  «    I    J     II 


—  18  — 

The  Degree  of  Motion  in  which  a  composition  is  to  be  executed 
is,  amongst  musicians,  ahuost  universally  indicated  by  the  Italian 
so-called  Tempo  Signs,  the  chief  of  which  are :  * 

1.  For  the  Slowest  Motion^  Largo,  Adagio,  Lento,  Grave. 

2.  For  Moderately  Slow  Motion^  Larghetto,  Andante,  Andan- 
tino. 

3.  For  Moderately  Fast  Motion^  K\^Q^XQ.tio^M.odiQX2A.o^  Allegro 
moderato,  Allegro  ma  non  troppo. 

4.  For  Fast  Motion^  Allegro,  with  various  additional  qual- 
ifying words,  as: — Allegro  con  moto.  Allegro  con  brio.  Allegro  con 
fuoco,  Allegro  animato.  Allegro  agitato.  Allegro  vivace,  Allegro 
appassionato.  Allegro  molto.  Allegro  assai. 

5.  For  the  Fastest  Motion^  Vivace,  Presto,  Prestissimo. 
These  signs  refer  to  the  tempo  of  the  whole  composition,  and  are 

written  at  the  beginning  of  it,  above  the  staff,  in  large  letters. 

The  following  signs  have  reference  to  a  certain  part  of  a  compo- 
sition,and  are  written  also  above  the  staff,  but  in  small  letters. 

They  are  : —  For  Slow  Tempo^  meno  mosso,  meno  moto,  meno 
allegro,  piu  lento. 

For  Faster  Tempo^  piu  mosso,  piu  moto,  piii  Allegro,  piu 
vivo,  piu  stretto. 

The  following  signs  refer  to  a  few  measures  and  are  written 
under  the  staff  in  small  letters.     They  are : 

Ritenuto,  ritardando,  rallentando,  calando  ;  indicating  a  slackening 
of  the  tempo. 

Accelerando,  stringendo  ;  a  hastening  of  the  tempo. 

A  tempo  or  tempo  primo ;  the  return  to  the  original  tempo. 

L'istesso  tempo  ;   the  same  tempo. 

Poco  a  poco ;  little  by  little  :  as  Stringendo  poco  a  poco,  means 
gradually  growing  faster. 

*  Some  German  composers  —  notably  Schumann  and  his  followers  —  have  not 
made  use  of  the  usual  Italian  tempo  signs,  but  of  their  German  equivalents. 
The  former  language  being  universal  amongst  musicians  is,  of  course,  preferable  in 
this  particular. 

Yet  the  student  of  music  is  recommended  to  make  himself  master  of  the  German 
language,  not  only  because  by  so  doing  he  opens  up  to  himself  a  world  of  interest  in 
connection  with  his  art,  but  because  without  a  knowledge  of  it  he  cannot  be 
thoroughly  familiar  with  the  literature  of  music.  Indeed,  those  looking  to  the  pro- 
feisionof  music  cannot  take  rank,  amongst  artists,  without  some  knowledge  of  it. 

—  Translator. 


—  19  — 


Colla  parte  means  that  all  the  accompanying  parts  are  to  subor- 
dinate themselves  to  one  part,  which,  for  the  moment,  is  to  be  made 
especially  prominent. 

Dynamic  Signs, or  those  which  determine  the  degree  of  the  force 
of  a  tone,  almost  without  exception,  appear  in  the  contracted  form 
of  the  words,and  are  written  under  the  notes  with  which  the  degree 
of  force  is  to  begin.  The  significance  of  these  signs  remains  until 
a  new  sign  appears.     They  are  : 

=  very  loud. 

=  loud. 

=  half  loud. 

=  soft. 

=  very  soft. 

=  increasing  in  volume. 

=  decreasing  in  volume. 

=  dying  away. 

=  losing  itself.      * 

r  refer  only  to  the  single  notes  un- 
=  -j  der  which   they  are    placed,  and 
(.  indicate  a  stronger  accent. 
Tones  in  music  are  divided  into   Whole  and  Half  tones. 
Half  tones  are  formed  by  tones  upon  neighboring  degrees  of  the 
staff,  between  which  no  third  tone  can  be  placed.* 

Chromatic  Signs.     The  signs  by  means  of  which  the  half  tones 
formed  from  the  original  seven  natural  tones  of  the  musical  scale, 
are  indicated,  are  called  Chromatic  signs.     They  are  : 
the  sharp, 
the  flat. 

the  double  sharp, 
the  double  fiat, 
the  natural  sign. 
The  %  raises  the  note  before  which  it  is  placed,  a  half  tone. 
The  1?  lowers  the  note  before  which  it  is  placed,  a  half  tone. 
The  X  raises  the  note  before  which  it  is  placed,  two  half  tones. 


ff 

fortissimo 

f 

forte 

mf 

mezzo- forte 

P 

piano 

PP 

pianissimo 

cresc. 

crescendo 

decresc. 

decrescendo 

dim. 

diminuendo 

morendo 

perdendosi 

sf. 

sforzato 

rinf. 

rinforzando 

X         = 

t?     = 


*  Formerly  theorists  talked  also  of  large  and  sviall  half  tones,  or  major  and 
minor  half  tones.  But  this  is  a  bit  of  pure  pedantry,  which  adds  nothing  to  the 
practical  understanding  of  the  subject. 


—  20  — 


The  \?\?  lowers  the  note  before  which  it  is  placed,  two  half  tones. 

The  tl  renders  the  sharp,  flat,  etc.,  before  a  note,  invalid,  and 
restores  it  to  its  natural  position  before  the  chromatic  sign  was  placed 
before  it. 

A  X  or  i?i?  demands  a  tfCf  to  remove  it.  If  a  note  has  had  a  x  or 
1?^  before  it  and  it  is  to  have  only  one  of  those  signs  removed,  one 
t]  is  placed  before  it  and  one  of  the  signs  required  —  i.e.  a  sharp 
or  a  flat. 


For  Example : 


Enharmonic  is  the  name  of  the  series  of  notes  by  which  the 
various  ways  of  writing  one  and  the  same  tone  are  indicated. 
Enharmonic  Table. 


Enharmonic  Tones. 


Simple  Tones. 


'—P7i 


=E=Ei^iS^^ 


ff^ 


^^p-^-^--^i3 


"zr 


Enharmonic 
Half  Tones. 


-Pf- 


^^=^=.^ 


1=5^^^=^^^ 


The  Scale  is  a  succession  of  tones  ascending  and  descending 
at  given  distances. 

Upon  examination  of  these  distances  it  will  be  found  that  fwo 
whole  tones  are  followed  by  one  half  tone,  then  three  whole  tones 
and  again  a  half  tone. 


ESI 


— y — , — 

11^111^ 

The   above    scale,    in   which    the  whole  and  half  tones   follow 
one  another,  after  the  formula  2^  and  3J,  is  called  the  Diatonic 


—  21  — 


Major   Scale,   and  from   its   initial  note  C,  C  Major or  the 

Scale  of  C  Major. 

If  the  Diatonic  Major  Scales  are  to  be  formed  upon  every  inter- 
val, of  course,  harmonic  signs,  flats,  sharps,  etc.,  must  be  brought 
into  requisition  in  order  to  preserve  the  proper  order  of  succession. 
Those  harmonic  signs  which  are  in  each  individual  case  essential  to 
the  formation  of  the  Diatonic  Major  Scale,  are  placed,  hov^ever,  not 
before  each  note,  but  at  the  beginning  of  the  w^hole  composition 
which  is  to  be  written  in  this  Key^  or  form  of  tone  coloring. 
These  signs  effect  the  whole  composition,  are  placed  at  the  begin- 
ning of  it,  and  are  called  the  Signature. 

Other  harmonic  signs,  appearing  in  the  course  of  the  composition 
extend  their  significance  only  over  a  single  measure. 


Table  of  Signatures  of  Major  Keys. 
C    Major  without  Signature. 
G       "       with  one  sharp,  f  sharp. 
D       "       with  two  sharps,  f  and  c  sharp. 
A       "       with  three  sharps,  f,  c  and  g  sharp. 
E       "       with  four  sharps,  f,  c,  g  and  d  sharp. 
B       "        with  five  sharps,  f,  c,  g,  d  and  a  sharp. 
Ftf     "       with  six  sharps,  f,  c,  g,  d,  a  and  e  sharp. 
CJf     "       with  seven  sharps,  f,  c,  g,  d,  a,  e  and  b  sharp. 
F    Major  with  one  flat,  b  flat. 
Bi?     ''       with  two  flats,  b  and  e  flat. 
Eb     "       with  three  flats,  b,  e  and  a  flat. 
A1?    "       with  four  flats,  b,  e,  a  and  d  flat. 
YP     "       with  five  flats,  b,  e,  a,  d  and  g  flat. 
Gt?    "       with  six  flats,  b,  e,  a,  d,  g  and  c  flat. 
Cb     ''       with  seven  flats,  b,  e,  a,  d,  g,  c  and  f  flat. 
Signatures  are  thus  indicated : 


-■m^^ 


—  22  — 

There  are  two  Minor  scales :   the  Harmonic  and  Melodic. 

Minor  scales  are  derived  from  major  scales  by  lowering  certain 
intervals  of  the  major  scale  of  the  same  name.  To  form  the  Har- 
monic Minor  Scale  of  C,  for  instance,  the  third  and  sixth  intervals 
are  lowered  in  C  major.     For  example : 

12345678 


i 


:l2t 


_ — , ^. 

The  Melodic  Minor  Scale  of  C,  by  lowering  the  third  in  ascend- 
ing and  the  seventh,  sixth  and  third  in  descending.     For  example  : 


i 


l^^,z=^,^=^ 


2===i=^ 


The  Signatures  of  minor  scales  are  derived  from  those  harmonic 
signs  which  appear  in  the  descending  melodic  minor  scale ;  as  C 
minor  with  three  flats,  bb,  eb,  a^. 

The  major  and  minor  scales  which  have  the  same  signatures  are 
called  Parallel  (or  relative  )  Scales. 

The  parallel  minor  scale  to  every  major  scale  is  found  upon  the 
third  interval  below  the  foundation  tone  or  initial  note  of  that  scale. 
For  example  Eb  major  has  C  minor  for  its  parallel,  both  having 
the  signature  three  flats. 

The  following  Circle,  called  the  Circle  of  Fifths,  from  the  regular 
progression  in  fifths,  of  the  successive  scales,  shows  the  proper 
arrangement  of  major  and  minor  keys, with  their  signatures. 


C**7 


—  23  — 


The  major  scales  are  on  the  outside  of  the  circle;  those  with 
sharps  to  the  right ;  those  with  flats  to  the  left ;  on  the  inner  side, 
are  the  minor  scales,  each  opposite  to  its  parallel  major  scale. 

The  marks  in  the  lower  part  of  the  circle  indicate  the  Enharmonic 
Scales. 

The  Chromatic  Scale  is  a  succession  of  half  tones,and  arises  from 
the  combinations  of  all  those  steps  and  half  steps  which  do  not  ap- 
pear in  the  Diatonic  Scale. 

In  order  to  avoid  a  superfluity  of  enharmonic  signs,  the  chromatic 
scale  is  so  written  that  in  ascending,  the  steps  belonging  to  the  origi- 
nal scale  are  raised  and  in  descending  they  are  lowered.  For  example : 


i 


^W^^' 


=^^,=^^w^-^^^^^^=^^. 


-•-^•-irb*^^ 


It  has  become  the  custom  amongst  theorists  to  give  fixed  names  to 
certain  tones  of  each  key,  for  the  purpose  of  clearness  in  the  study 
of  harmony  and  of  musical  form. 

The  initial  note  or  Foundation  Tone  of  every  key,  is  called  The 
Tonic;  the  fifth  tone  ^(^i?!;^  the  foundation  tone.  The  Uf per  Domi- 
nant; the  fifth  tone  below  the  foundation  tone,  The  Lower  Domi- 
nant^ or  Sub- Dominant ;  the  third  tone  above  the  foundation  tone, 
The  Upper  Mediant;  the  third  tone  below  the  foundation  tone, 
The  Lower  Mediant;  the  seventh  tone  of  the  scale  is  called  The 
Leading  Note. 

The  following  formula  shows  the  above  terms  as  applied  to  C  major. 


lOiV£'/?  MSDfANT 


UPPER  _  nEDIAt4T 


—.24  — 

An  Interval  is  the  distance  from  one  tone  to  another.  Inter- 
vals are  divided  into  Major,  Minor,  Augmented  and  Diminished. 

A  minor  interval  is  a  half  tone  smaller  than  a  major ;  an  aug- 
mented interval  a  half  tone  larger ;  a  diminished  interv^al  two  half 
tones  smaller.* 

In  the  Diatonic  Major  Scale  all  intervals  formed  with  the  tonic  as 
their  basis,  are  major  intervals ;  if,  therefore,  any  interval  is  to  be 
measured,  the  lowest  tone  of  it  is  to  be  considered  as  the  tonic  of  a 
diatonic  major  scale, and  if  the  upper  tone  of  it  lies  in  that  scale,  it 
is  a  major  interval ;  if  it  is  a  half  tone  smaller,  it  is  a  minor  inter- 
val ;  a  half  tone  larger,  an  augmented  interval ;  two  half  tones 
smaller,  a  diminished  interval. 

The  Names  of  the  Intervals  are  Primes  or  Unison,  Seconds, 
Thirds,  Fourths,  Fifths,  Sixths,  Sevenths,  Eighths  or  Octaves, 
Ninths  and  Tenths. 

Hence,  for  example  :  the  interval  C  —  A  would  be  a  major  sixth 
because  the  sixth  tone  in  C  major  is  A ;  C  —  At^  a  minor  sixth  ; 
C  —  At?l^  a  diminished ;  C — Ajt  an  augmented  sixth.  If  the  lower 
tone  of  an  interval  to  be  classified,  is  ft?,  g:f,  d#,  ajf  or  e#  —  upon  which 
it  is  not  customary  ( though  it  would  be  possible)  to  form  diatonic 
major  scales  —  the  quickest  way  to  decide  their  distances  is  to  trans- 
pose the  lower  tone  by  means  of  enharmonic  signs  :  as,  for  instance, 
if  f  17 —  at>  is  required,  transpose  ft>  into  e  and  ai?  in  gj  and  then  re- 
garding E  as  the  tonic  of  the  diatonic  major  scale  E,  fromE  —  g^  is 
a  major  third;  in  like  manner  b#  —  a,  is  transposed  into  c  —  bW? 
and  becomes  a  diminished  seventh.  The  Examples  under  letter  A 
at  the  end  of  the  book  are  to  be  marked  out  by  the  pupil. 

Chords. 

A  chord  is  the  simultaneous  sound  of  three  or  more  tones  placed 
in  thirds,  one  above  another. 

The  Major  Triad  consists  of  the  foundation  tone,  its  major  third 
and  its  major  fifth.  In  looking  for  the  major  triads  in  every  key, 
one  finds  that  they  occur  upon  the  ist,  4th  and  5th  degrees  of  the 
scale  in  major  keys,and  upon  the  5th  and  6th  degrees,  in  minor  keys. 

The  Minor  Triad  consists  of  the  foundation  tone,  its  minor  third 
and  its  major  fifth.     It  is  formed  in  major  keys,  upon  the  2d,  3d  and 

*  Many  theorists  call  the  major,  prime,  fifth,  fourth  and  octave,  perfect  intervals  ; 
and  the  minor  fifth,  imperfect  or,  diminished;  the  names  used  above  are  certainly 
simpler  and  more  consistent. 


—  25  — 


6th  degrees  of  the  scale  ;   in  minor  keys,  upon  the  i  st  and  4th  degrees. 

The  Augmented  Triad  consists  of  the  foundation  tone,  its  major 
third  and  its  augmented  fifth.  It  is  found  only  in  minor  keys  and 
upon  the  third  degree  of  the  scale. 

The  Diminished  Triad  consists  of  the  foundation  tone,  minor 
third  and  minor  fifth.  It  is  found  upon  the  7th  degree  of  the  scale 
in  major, and  the  2d  and  7th  in  minor  keys. 

The  following  shows  the  relative  positions  of  all  the  triads  in 
major  and  minor  keys. 
C  major. 


m 


1 

MAJOR 


2 

MINOR 


3 

MIN. 


4 

MAJ. 


5 

MAJ. 


6 

MIN. 


C  minor. 


7 

DIMINISHED, 
(^ 


^ 


12  3 

MINOR    DIMINISHED    AUGMENTED 


4 

MIN. 


5 

MAJ. 


G  7 

MAJ,    DIMINISHED. 


Every  interval  of  a  triad  can  be  doubled,  i.  e.  it  can  appear  at  the 
same  time  in  different  octaves,  or  in  different  voices  of  the  same 
octave.     For  example : 


:|-g— l^-gj 


r 


-f- 


IS 


-<$*--^»-         -<5>-  -<&-  -G>- 

In  writing  chords  with  their  four  parts,  the  foundation  tone  of 
the  triad  is  most  frequently  doubled ;  more  rarely,  the  third  or  the 
fifth.  If  the  3d. lies  in  the  uppermost  part,  (or  voice)  the  position 
of  the  triad  is  called  the  position  of  the  third ;  if  the  5th,  the  posi- 
tion of  the  fifth ;  etc. 


J-      <2 

^^ 

&' 

7» 

Tn 

^j 

^ 

-^ 

t 

\         <-j 

^ 

<? 

ri 

G 

>         <^ 

ej 

r^ 

^ 

0 

(J> 

-<s- 

c-\  • 

^^ 

*-i. 

'^ 

y        .^ 

^ 

Position  of  the  3d. 

Pos.  of  the  5th. 

PoB.  of  the  Octave. 

Pos.  of  the  3d. 

Pos.  of  the  5th. 

Pos.  of  the  Octave. 

Thorough  Bass  is  simply  the  Stenography  of  Harmony. 

In  thorough-bass  writing  of  chords,  a  bass  note  without  any  fig- 
ure above  or  below  it  denotes  that  the  triad  of  this  note  is  meant. 
A  sharp.,  Jlat  or  natural  sign,  above  or  below  the  bass  note  (  with- 
out a  figure  )  refers  to  the  3d.  of  the  chord  demanded.  If  any 
other  interval  is  to  be  raised.,  the  numeral  designating  it  is  placed 


—  26  — 

above  or  below  the  bass  note,  and  a  mark  drawn  through  it ;  if  it 
is  to  be  lowered,  the  necessary  sign  Is  placed  before  the  numeral. 
For  example : 


i^       0       tt        t^5 


The  line  at  b  denotes  that  the  same  harmony  is  to  continue  as  far 
as  the  line  extends. 

The  letters  t.  s.  at  c,  stand  for  the  Italian  words,  tasto  solo,  and 
denote  that  the  bass  is  to  have  no  harmony  played  with  it.  Other 
figuring  of  chords  will  be  given  as  they  appear  in  the  course  of  the 
examples. 

The  chief  rule  in  combining  chords,  is  the  following :  Common 
tones  should  be  kept  in  the  same  voice  and  octave  ;  the  other  tones 
should  move  as  little  as  possible. 


t»i=i 


^iSi^^^ 


w 


rg^^ 


-^    0-^0 


.0 — 0—10- 


^;=?^t 


•:^::^i=iSi=:5S 


• — S^S     0r^^0 — •— ^* 


m 


!St3£EE*gsgfelikfeE| 


-# W 


ll    ^/^r     V    ^t^_:^ 


^i 


r 


9 


In  the  above  example,  the  bass  note  is  doubled  in  every  triad. 


*  When  chords  are  to  be  written  which  demand  notes  outside  the  staff,  they  are 
denoted  by  means  of  added  lines  as  in  the  chord  of  F  major  above.     The  same 


chord  below  the  staff  would  be  written  thus 


i 


27- 


Common  tones  are  connected  by  curved  lines  ( or  ties  ) . 

Other  examples  of  this  kind  will  be  found  in  the  Appendix  under 
B^.  If  there  are  no  common  tones,  lead  the  voices  in  opposite 
directions;  /.  ^.,  the  three  upper  voices  in  the  opposite  direction 
from  the  bass. 


I^^g^^^^^^^g 


^ff^^^fesN^^^sJ^^ggjI 


^^^^^=i^^^m 


ga 


In  the  above  example,  common  tones  are  bound  together,  and 
where  there  are  none  alike,  straight  lines  show  the  opposite  direc- 
tions in  which  the  parts  move. 

Further  examples  are  to  be  found  under  C. 

The  next  rule  arises  from  the  necessity  of  avoiding  false  progres- 
sions. False  Progressions  are  the  simultaneous  movement  of  two 
or  more  voices  in  octaves,  fifths  or  fourths. 


At  the  example  marked  a,  the  bass  and  the  fifth  in  both  chords, 
move  in  the  same  direction ;   also  the  bass  and  its  octave. 

At  example  b,  there  are  successive  fourths ;   at  c,  the  outer  voices 

*  The  student  is  advised  to  write  each  exercise  in  the  three  different  ways,  indi- 
cated above,  following  the  same  principle  as  to  the  doubling  of  the  bass-note  and 
the  leading  of  the  voices.  Constant  practice  in  playing  the  harmony  to  each  of 
the  basses  given,  without  writing  them  out  upon  paper,  is  of  the  greatest  importance. 


—  28  — 

b  bt>,  made  what  is  called,  in  harmony,  Cross  Position.  This  oc- 
curs when  neighboring  tones  upon  the  same  degree  of  the  staff 
appear  in  two  successive  chords,  in  different  parts  or  voices.  If, 
however,  one  part  has  both  tones,  ( as  in  example  d )  the  cross 
position  no  longer  exists,  as  in  the  above  example,  where  the  upper 
voice  has  b  as  well  as  bb  and  the  bass  has  bl?. 

Progressions  like  the  following  example  make  the  impression 
of  being  consecutive  Octaves,  Fifths  and  Cross  Position,  without,  in 
the  strictest  sense  of  the  word,  being  false.  They  are,  therefore, 
called  Concealed  Octaves,  Fifths,  etc.,  and  are  to  be  as  carefully 
avoided  as  direct  octaves,  fifths,  etc.* 


^       a     mm  .        I  '^1        J  b       I        I        I        I  C        I— *''T^  , 


Exceptions!  to   the   rule   against  the  use  of    successive  Fifths, 
Fourths,  etc. 

1.  The  minor  5th  may  follow  the  major  5th.^ 

2.  The  augmented  4th  may  follow  the  major  4th. 

3.  Fourths,  above  or  below  which,  another  voice  proceeds  in 
successive  thirds,  fnay  follow  one  another. 


2 


#-;-i=pg=g-8-g^>-*-^-^#-H 


=^-fel= 


*  Progressions  of  Seconds,  Sevenths  and  Ninths  are,  of  course,  to  be  as  care- 
fully avoided  as  those  just  mentioned ;  but  they  are  so  extremely  disagreeable  to 
the  ear,  as  may  be  readily  proved  by  trying  them  upon  the  piano,  that  there  is  little 
danger  of  their  appearing,  and  there  are,  therefore,  no  especial  rules  against  their 
use. 

t  As  the  rule  against  the  use  of  consecutive  octaves,  etc.,  is  solely  for  the  sake 
of  beauty  of  sound,it  is  not  to  be  observed  when  successive  5ths,  4ths,  or  even 
Cross  Position  sound  well;  as  for  instance  in  the  following  succession  of  chords. 


—  29  — 

Doubled  Octaves,  as  they  constantly  appear,  especially  in  orches- 
tral    compositions,    are    not   to    be   confounded    with    consecutive 

Octaves. 

a  b  c 


-<$>- 


-4-  ^  -&  ^ 


At  a  there  is  a  Doubling  of  the  bass. 
At  b  there  is  a  Doubling'  of  the  upper  voice. 
At  c  there  is  a  Doubling  of  the  middle  voice ;  but  in  all  these 
cases  there  is  no  false  progression. 


Inversion. 

If  the  several  tones  of  a  chord  are  so  placed  that  another  than  the 
foundation  tone  lies  in  the  bass,  this  is  called  inverting  the  chord. 

The  First  Inversion  of  the  Triad  is  that  in  vvrhich  the  third  of  the 
Triad  lies  in  the  bass.  It  consists  of  bass-tone,  third  and  sixth,  is 
called  the  chord  of  the  6th  and  is  figured  6. 

In  four-part  harmony  the  6th  interval  of  the  chord  of  the  6th  is 
most  frequently  doubled,  more  rarely  the  3d,  most  rarely  the  bass- 
note. 

a  b  c 


ISZW. 

-• — 


i 


-#-#- 


-#-•- 


m. 


-#-•- 


;i 


I 


9i 


The  above  example  show^s  the  chord  of  the  6th,  first,  at  a,  v^ith 
doubled  sixth ;  secondly,  at  b,  vs^ith  doubled  third ;  thirdly,  at  c, 
with  doubled  bass  tone. 

It  is  advisable  in  the  first  exercises  to  be  worked  out  by  the  pupil, 
to  make  use  of  that  doubling  of  the  sixth  which  produces  the  most 
agreeable  effect  upon  the  ear. 


—  30 


For  example  r 


N.B. 


iga, 


H 


6  6 


As  Contrary  Motion  is  always  to  be  sought,  it  is  well  to  make 
use  of  it  even  at  times  when  the  successive  chords  contain  common 
tones :  as  for  instance  in  the  chords  of  the  6th  upon  cj,  b,  a  and  g, 
in  the  above  example. 

As  the  bass  in  these  instances  always  proceeds  by  one  degree 
upward^  the  sixth  in  the  lower  voice  should  be  kept  stationary,  and 
the  three  other  voices  proceed  downward — not,  as  in  the  following 
example,  which  would  not  be  so  good  because  such  a  succession  as 
is  indicated  by  the  marks,  would  produce  the  effect  of  concealed 
octaves. 


6  6 

For  the  same  reason  the  d,  in  the  chord  of  the  6th  upon  f  jf  is 
held,  in  both  voices  as  at  n.  b.  instead  of  carrying  it  on  to  g,  so 
that  a  triad  with  doubled  fifth  is  produced.  Further  examples  are 
to  be  found  in  the  Appendix  D. 

If  several  chords  of  the  6th.follow  one  another,  false  progressions 
are  avoided  by  doubling  the  sixth  and  the  bass-note  alternately ;  or 
by  leading  the  chord  of  the  sixth  in  contrary  motion  and  doubling 
the  bass-note  several  times.  By  sometimes  doubling  the  third  the 
disposition  of  the  chords  can  also  be  improved. 


—  31  — 


For  example 


^^ 


£E 


:^E?:4^^33^:i:^ 


In  this  example,  six  successive  fourths  appear  in  the  first  and 
the  second  staffs,  but  the  bass  notes  to  which  they  belong  go  in 
thirds  to  one  of  the  voices  of  the  chord,  and  thus  the  false  progres- 
sion is  done  aw^ay  w^ith.  The  othei*  remaining  voice  of  the  three, 
changes  vs^ith  the  doubling  of  the  sixth  and  the  bass-note,  in  order 
to  avoid  consecutive  Octaves  and  Fifths.  In  the  third  ^X.di'^^contrary 
motion  prevails ;  in  the  second  and  third  chords  of  the  6th,  the  bass 
note  is  to  be  found ;  in  the  fourth  chord,  the  third  appears ;  in  the 
fifth  the  bass-note  again  and  in  the  sixth  chord,  the  sixth  is  doubled. 

The  chord  of  the  6th  of  the  Diminished  Triad,  on  the  other 
hand,  is  especially  agreeable  w^ith  the  doubled  bass-note^  but  it 
frequently  also  appears  with  doubled  third  and  with  doubled  sixth. 

For  example : 


^ 


i^iB^e 


•-tT 


§± 


^m. 


m 


6  6  6  6  6 

At  c,  there  are  consecutive  Fourths  in  the  middle  voices,  which 
by  the  descending  of  the  F  (  in  the  upper  voice  )  to  E,  produces  an 


*  A  succession  of  chords  of  the  6th  may  also  be  figured  thus 


^^^ 


—  32-- 

agreeable  effect;  at  D,  the  upper  b  ascends  toward  C,  and  the 
lower  b  descends  towards  G,  because,  otherwise,  the  outer  voices 
would  produce  the  effect  of  Concealed  Fifths.  The  handling  of 
the  chords  at  e  is  also  frequently  to  be  met.  Further  examples  in 
Appendix  E. 

It  is  also  most  beneficial  for  the  student  to  practice  writing  fig- 
ured basses  in  the  broad  (or  open)  position  of  the  chords;  /.  e.^ 
beyond  the  scope  of  an  octave  —  making  use  of  the  three  C  clefs ; 
as,  for  example,  in  the  following : 


P 


T-i — -F— FF — ^- 


£2. (2. 


-^ 


(g |g ttg. 


I 


^ 


^Ei 


& &- 


V^ 


^■- 


-&- 


i=B 


-^- 


■«) 12- 


I 


EEe^£ 


3EEEE=t 


-^ 


E; 


^^=t 


ii3 


e-te 


:b 


±=^=^ 


:p: 


Further  examples  in  Appendix  F. 

The  Second  Inversion  of  the  Triad  is  the  6  chord,  in  which  the 
Fifth  of  the  Triad  lies  in  the  bass.  It  consists  of  bass-tone^  fourth 
and  sixths  is  figured  6  or  4  and  appears  in  four-part  harmony,  al- 
most always  with  doubled  bass-tone.  The  chief  exception  to  this 
rule  is  in  the  ^  chord  of  the  Augmented  Triad,  when  the  bass-tone 
should  not  be  doubled  as  otherwise,  consecutive  octaves  are 
almost  unavoidable,  as,  for  example  at  N.B.  in  the  following 
exercise:  ' 


—  33  — 


^^^^l^&=i^^^ElEl^^^^H 


-#--#--#--#-  -•#-  -##-  -••-   •^  5-  ^  T   '^  5= 


-Ci^ — 

— •- 

-•- 

-•— 

-•- 

N.B. 



II 

^^%- 

. 

:i*z: 

— •— 

IMZ 

--»- 

=i?«= 

-•- 

z*z 

_•_ 

-JXZ 

-9- 

-»- 

^ 

i 


i   i 


When  a  triijd  is  to  be  played  upon  a  bass-note  which  has  just 
before  appeared  in  figured  form,  the  second  of  the  two  is  to  be 
marked  with  the  numbers  £,  as  is  shown  in  the  preceding  example 
several  times. 

The  5  chord  or  chord  of  the  Fifth  and  Fourth  is  not  to  be  re- 
garded as  an  independent  chord  at  all,  but  as  a  preparation  for  a 
major  or  minor  triad,  or  a  chord  of  the  Dominant  Seventh  upon 
the  same  degree  of  the  Staff.  It  consists  oi  foundation  tone,  major 
Jifth  and  major  fourth.  The  foundation  tone  is  almost  without 
exception  the  tone  to  double.* 


i 


^—^ 


iff 


-#-     -^-     -^   w^     .^ 


^ 


m 


Further  examples  of  the  ^  and  the  5  chords  in  the  Appendix  G. 

*  The  inversions  of  the  £  chord  are  even  more  than  the  original  chord,  of  a 
preparatory  nature.  They  sound  like  suspended  6  or  ^  chords,  have  no  especial 
name,  and  are  figured  f  or  f ,  as  the  case  may  be. 


—  34  — 


The  Chord  of  the  Dominant  Seventh, 

If  to  the  Triad  of  the  Upper  Dominant  a  third  ( the  third  pecul- 
iar to  the  natural  progression  of  the  scale,  of  which  it,  in  each  case, 
forms  a  part  )  be  added,  the  chord  thus  produced  is  called  the 
chord  of  the  Dominant  Seventh,  which  consists  o^ foundation  tone^ 
major  third,  major  fifth  and  minor  seventh,  and  is  figured  7.  This 
exceedingly  important  chord  necessitates  the  following  of  another 
chord  upon  it,  and  this  enforced  succession  is  called  its  Resolution. 

The  proper  resolution  of  the  chord  of  the  Dominant  Seventh  is 
as  follows :  \\\q  foundation  tone  proceeds  a  fourth  upward  or  a 
fiftJi  downward^  but  may  also  remain  stationary.  The  third  goes 
one  degree  upward^  the  ffth  and  the  seventh  one  degree  down- 
ward; the  ffth^  however,  may  upon  occasion,  proceed  ?^pward. 
From  this  resolution,  in  which  the  fifth  proceeds  downward,  an  in- 
complete triad  is  produced,  with  twice-doubled  foundation  tone  and 
third,  as  in  a  and  b ;  if  the  foundation  tone  remains  stationary,  a  g 
chord  is  produced  with  doubled  fourth,  as  in  c. 


/ 

^      a                   b                     c                         d                       e             ^ 

7f         •    1    •     ••"!             1    •     *    1    •    ^*  Fl 

St—' -I—' — -I—* — •— 1 1 +1 

\\ 

^ =1 ^1 — l=i^M^r-^J 

7                              7                              7           6                 7                             7         be 

When  the  fifth  goes  upward^  as  at  d,  an  incomplete  triad  with 
doubled  foundation  tone  and  doubled  third  is  the  result.  At  e,  the 
fifth  proceeding  upward^^.  6  chord  with  doubled  sixth  is  the  result. 
As  the  chord  of  the  Dominant  Seventh  is  the  same  in  major  and 
minor  (the  harmonic  minor  scale  is,  of  course,  meant),  it  can  be 
resolved  into  minor  as  well  as  major,  as,  for  example,  at  e. 


g^^^^^^^^^^^^^^S^H 


S 


^i: 


-^-r\ 


f  ^  I 


%  I 


Further  examples  in  Appendix  H. 


—  35  — 

The  Inversions  of  the  Dominant  Seventh  chord  are  resolved  after 
the  same  rule  as  the  original  chord,  except  the  foundation  tone, 
which  in  the  inversions,  always  remains  stationary. 

The  JFirst  Inversion  is  the  chord  of  the  Fifth  and  Sixth,  which 
•consists  of  bass-tone^  minor  thirds  minor  Jifth^  and  minor  sixth,, 
and  is  figured  §  or  g. 

Example  as  follows : 


"^^^^^^^^^ 


9^— » •        m   —• ^ #— »      ^  H 


5  0 

«  % 

7 


Further  examples  in  Appendix  I. 

The  Second  Inversion  of  the  chord  of  the  Dominant  Seventh,  is 
the  Chord  of  the  Third  and  Fourth,  consisting  of  bass  tone,  minor 
third,  major  fourth  and  major  sixth  and  is  figured  3  or  ^. 


i 


^?^s^;^1=|=5_=ES^3=^l 


m^^^^^^^^^m 


1    "I 


t 


In  the  preceding  example,  the  bass  tone  of  the  three-four  chord 
is  generally  carried  downward.  As  it,  however,  is  the  Jiftk  of  the 
original  chord,  it  can,  like  it,  move  one  degree  upward.  In  the 
chord  of  the  sixth  thus  produced,  the  doubling  of  the  bass  note  should 
be  avoided  by  taking  the  third  of  the  3  chord  a  fourth  downward  ; 
but  this  is  not  to  be  done  when  it  lies  in  the  upper  voice. 


—  36 


m 


w  —  • 


t=A 


ESl 


^^ 


i 


ij 


It — 5 — '•—'r 

^ — • — ^    ^# 


i»^^g-»^=Fl=»=H=1=» 


fe:5^=^F^;^^^k3^i;S=j={=t=^ 


i 


as 


Further  examples  in  Appendix  K. 

The  Third  Inversion  is  the  chord  of  the  Second,  which  consists 
of  bass-tone,  major  second,  augmented  fourth  and  major  sixth,  and 
is  figured  2.  The.  resolution  of  the  chord  of  the  second,  results 
without  exception  in  a  chord  of  the  ^ixth,  upon  the  degree  or  half 
degree  below  it. 


#      #      #      •     #     •     9     9      •      #     •         •— p  _^ 


IB 


9^^^ 


Eg 


263  26666  5     -• 

4  4         6  4       7 

Further  examples  in  Appendix  L. 

Besides  the  regular  resolution  of  the  chord  of  the  Dominant 
Seventh  there  are  others,  which,  however,  relate  only  "to  the  origi- 
nal chord  and  not  to  the  inversions.     For  instance  ; 

1 .  The  third  may  proceed  a  third  downward. 

2.  The  three  upper  voices  may  proceed  one  degree  upward, 
if  the  seventh  lies  in  a  middle  voice. 

3.  The  fifth  may  be  left  out  and  the  bass-note  doubled  instead 
of  it,  which  then  remains  stationary  in  the  resolution. 

This  last  manner  of  treating  the  chord  of  the  Dominant  Seventh 
is  the  most  agreeable  to  the  ear,  and  the  most  convenient  for  the 
handling  of  the  other  parts  of  the  chord.     All  of  these  exceptional 


—  37  — 


resolutions  of  the  chord  of  the  Dominant  Seventh  have  the  advan- 
tage of  producing  a  complete  triad,  that  is,  one  in  which  all  the 
interv^als  appear. 


First 


\ 


^ 


Second. 


N.B. 


^3^^j 


Third 
Exceptional 
Resolution 
OF  THE  Chord 
OF  THE  Domi- 
nant Seventh. 


i 


^. 


i^rrrS: 


H 


t 


At  N.  B.  if  the  three  upper  voices  were  taken  upward,  consecu- 
tive fifths  would  appear ;  therefore,  in  this  case  (  where  the  seventh 
does  not  lie  in  the  middle  voice  )  the  regular  resolution  (  as  used 
above)  or  the  first  exceptional  one  is  preferable.  It  is  advisable 
for  the  pupil  to  write  the  exercises  upon  the  chord  of  the  Dominant 
Seventh,  first  with  the  regular  and  then  with  the  three  irregular 
resolutions. 

Examples  for  this  purpose  are  to  be  found  in  Appendix  M. 

If  a  third  ( that  third  which  pertains  to  the  scale  to  which  the 
chord  itself  belongs )  be  added  to  the  Chord  of  the  Dominant 
Seventh^  a  chord  is  formed  which  is  called  the  Chord  of  the 
Ninth: — in  major,  the  Major  Chord  of  the  Ninths  in  minor,  the 
Minor  Chord  of  the  Ninth :  it  consists  of  foundation  tone,  major 
3d,  major  5th,  minor  7th,  and  major  or  minor  9th  and  is  figured  9. 

The  resolution  of  the  chord  of  the  ninth  is  the  same  as  that  of 
the  chord  of  the  Dominant  Seventh,  but  the  ninth  always  moves 
one  degree  downward ;  the  fifth,  however,  which  in  the  Dominant 
Seventh  may  move  upward  or  downward,  in  the  Chord  of  the 
Ninth  must  move  upward^  when  it  lies  under  the  ninths  as  it 
otherwise  would  make  a  false  progression  oi  fifths  with  it.  In 
four-part  harmony,  however,  the  fifth  is  omitted  altogether. 


—  38  — 


fe^^^^^^j,^ 


^ 


i 


^« 


if: 


±»a: 


^EE^^l^^yJ: 


I 


i 


-bt 


w 


b9 


"¥i 


The  student  should  note  the  fact,  that  the  resolution  of  the  major 
chord  of  the  9th  is  only  in  major,  while  that  of  the  minor  chord  of 
the  9th  is  in  both  minor  and  major.  In  order  to  become  familiar 
with  the  treatment  of  the  fifth,  the  student  is  advised  to  write  the 
chord  of  the  9th  in  both  four  and  five  part  harmony,  as  in  the  fol- 
lowing example : 


^^^^^^^^^^^^ 


3^^^^tzg.^^^j^^^;^J 


w- 


EP 


I 


I 


"I 


Further  examples  in  Appendix  N. 

The  Inversions  of  the  chord  of  the  9th  are  resolved  after  the  same 
manner  as  the  original  chord;  because  of  the  accumulation  of  very 
closely  neighboring  tones,  however,  some  positions  are  not  allow- 
able ;  while  others,  on  the  contrary,  are  not  only  allowable,  but 
agreeable. 


—  39  — 

The  First  Inversion  Is  the  chord  of  the  Sixth  and  Seventh,  which 
consists  of  bass-tone,  fifth,  sixth  and  seventh  and  is  figured  ^  or  7 
The  most  agreeable  position  of  this  chord  is  the  following ;   the  6th 
next  to  the  bass-tone  and  the  5th  and  7th  in  the  octave  above  it. 


i 


5^S?EEtf: 


31^ 


f*z:l2f: 


:l2i: 


3^r 


s 


Jl^^^=ffj^^l 


9r 


Bad. 


Good. 


Less  agreeable,but 
frequently  used. 


The  progression  of  ^q  foundation  tone  of  the  original  chord  at 
e,  though  possible,  is  rare. 

The  Second  Inversion,  is  the  chord  of  the  Third  and  Second, 
which  consists  of  bass-tone,  second,  third  and  fourth,  and  is  figured 

The  most  agreeable  position  is  the  following :  bass-tone,  second, 
fourth  and,  above  them,  the  third.  The  resolution  of  the  2  chord 
is  upon  the  chord  of  the  6th  of  the  next  degree  below  it  or  the 
half  degree  above  it. 


\z=u=t^^=t==i=^^'f^^^i^}'fM=di=^ 


bi        6 


bi 


J^^ 


9i 


ic 


Bad.  Good.  Less  agreeable,  but 

frequently  used. 


The  Third  Inversion  is  the  chord  of  the  second,  the  sixth  and 

the  seventh,  which  consists  of  bass-tone,  second,  sixth  and  seventh, 

2         7 
and  is  figured  6.  or  6. 

The  most  agreeable  position  is  that  in  which  the  intervals  follow 
one  another  in  the  order  of  the  figuring  of  the  bass.  The  resolu- 
tion is  into  the  g  chord  upon  the  degree  below  it. 


40  — 


l=E.^=^ 


B 


p^ 


w 


I    I 

7 


I     i"! 


IB 


The  following  is  an  example  of  the  inversions  of  the  chord  of 
the  9th ; 


^^^^E^^^gi^B 


m 


9il: 


i 


7 


Further  examples  in  Appendix,  under  O. 

The  Inversion  of  the  chord  of  the  ninth,  in  which  the  Jifth 
lies  in  the  bass,  is  only  agreeable,  when  the  five  parts  are  repre- 
sented ;  as  in  the  following  example  : 


i^jfe^B 


^B 


If  the  foundation  tone  of  the  major  and  the  minor  chords  of  the 
9th  be  left  out,  a  chord  is  formed  which  is  called,  in  the  one  case, 
the  Minor  Chord  of  the  Seventh ;  and  in  the  other,  the  Diminished 
Chord  of  the  Seventh. 

The  Minor  Chord  of  the  7th  consists  of  foundation  tone,  minor 
third,  minor  fifth  and  minor  seventh. 

The  Diminished  Chord  of  the  7th  consists  of  minor  third, 
minor  fifth  and  diminished  seventh. 

Both  chords  are  figured  7,  and  are  treated  as  parts  of  the  chord 


—  41  — 


of  the  9th.  The  rule  with  regard  to  the  fifth  In  the  chord  of  the  9th, 
when  it  lies  under  the  9th,  is,  in  the  altered  enumeration  of  the 
intervals,  in  the  case  of  these  chords  of  the  7th  —  as  follows:  the 
third  oi  the  minor  and  the  Diminished  chords  of  the  7th,/«^^5/ move 
upward^  when  it  lies  under  the  7th. 


1^: 


3^^ 


9i 


Major  Ch'd  of 
the  9th. 


Minor 


Ch'd  of 


the  7th. 


b9 

Minor  Ch'd  of 
the  9th, 


i 


±& 


g 


-'^- 


NSE^ 


-i^ 


9i 


9 


Ch'd  of  the  Diminished  7th. 


L^ 


b7 


The  Chord  of  the  Diminished  7th  like  the  minor  chord  of  the 
9th,  from  which  it  is  derived,  can  be  resolved  into  both  major  and 
minor.  Both  chords  —  the  minor  and  the  diminished  chords  of  the 
7th  —  have  three  inversions,  the  5,  the  3  and  the  2  chord,  the  tones 
of  which  move  in  the  same  direction  as  each  does  in  the  original 
chord. 


i^sSil^il^iSili^^^B 


B 


^ 


-•-^-•—w-\ 


^ 


7  7  56  3636  3636  36 

In  b,  as  the  third  of  the  original  chord  b,  d,  f,  a,  lies  in  the  bass, 
the  seventh  must  always  lie  above  it,  and  the  bass-note  be  led  up- 
ward. 


—  42  — 

In  the  two  chords  of  the  2d  there  is  at  d,  first  a  regular  and  then 
an  exceptional  treatment  of  the  chord,  in  which  d  moves  upward, 
although  it  lies  above  a ;  this  is  caused  by  the  fact,  that  there  would 
otherwise  be  a  false  progression  oi  fourths  with  no  third  voice 
proceeding  in  thirds  alongside  it. 

It  is  customary  to  use  the  rule  exemplified  at  e  rather  than  that  at 
jd,  because  it  produces  a  more  agreeable  6  chord. 

If  uncertainty  arises  as  to  the  best  method  of  treating  these  chords 
of  the  7th  (which,  it  must  always  be  remembered,  are  derived 
from  the  chord  of  the  9th),  it  is  well  to  place  the  intervals  com- 
posing them,one  above  another  in  thirds,  and  then  add  a  major  third, 
below  the  bass-tone,  when,  the  chord  of  the  9th,  from  which  it  is 
derived,  thus  being  formed,  the  treatment  of  the  intervals  will  be 
clear. 


|E£Er^^E^^'^^|E^t^E!EgEf| 


W- 


-3 • 


S 


7  5626363  P3  6 

Further  examples  in  Appendix  P. 

The  following  table  furnishes  a  view  of  all  the  chords  thus  far 
mentioned,  with  their  derivations : 

Table  of  Chords. 

The  Triad. 

in  minor  keys. 


IN   MAJOR  KEYS. 

Major  triad  upon  the  intervals  i , 

Minor  triad  upon  2,  3,  6. 
Diminished  triad  upon  7. 


Upon  5,  6. 
Upon  1,4. 
Upon  2,  7. 
Augmented  triad  upon  3, 


Inversions  are  the  6  and  the  g  chords. 
The  5  chord. 


—  43  — 


The   Chord  of  the  Dominant  Seventh. 
Figured  7* 


Inversions  are  §,  3  and  2  chords. 


6'  4 


Major  Chord  of  the  9th. 
Figured  9. 


Minor  Chord  of  the  9th. 
Figured  9. 


Inversions  are  §,  3  and  6  chords. 

I     z  7 


Minor  Chord  of  the  Seventh. 
Figured  7. 


Dim.  Chord  of  the  Seventh. 
Figured  7* 


Besides  these,  there  are  jive  chords  of  the  Seventh,  which  are 
derived  by  altering  the  intervals  of  the  Dominant  Seventh  and  the 
Diminished  Seventh.      These  are  called  Mixed   Chords. 

The  First  Mixed  Chord  is  derived  from  the  Dominant  Seventh 
chord  by  the  low^ering  of  its  third.,  so  that,  for  example,  from  g,  b, 
d,  f,  the  mixed  chord  g,  bb,  d,  f  is  produced.  The  treatment  of 
it  is  explained  in  the  following  example : 


5=M^ 


b       -•- 


7  b?  7  6 


i^; 


u 


be 


b7 


g 


i 


The  Inversions  of  the  Mixed  chords  of  the  Seventh  have  the 
same  names  as  those  of  the  other  chords  of  the  Seventh.  They 
are  to  be  dealt  with  as  are  the  original  chords ;  in  e,  for  example, 
the  manner  of  resolving  the  5  chord  is  based  upon  that  at  a,  in  its 
original  form.  The  foundation  tone  in  the  resolution  of  the  in- 
versions of  the  mixed  chords,  remains  stationary,  as  it  does  in  those 
of  the  Dominant  Seventh. 

The  Second  Mixed  Chord  is  also  derived  from  the  Dominant 

7th  by  the  lowering   of  the  fifth ;    from  g,   b,   d,  f ;  g,   b,   d{7,   f 

is  produced.      This  chord  most  frequently  appears  in  its  second 

inversion  as  3  chord. 
4 


—  44  — 


-^t=^ 


^=^ 


^ 


^5f 


^^ 


-.— ^- 


*4 


'i 


S 


i    bi 


The  Third  Mixed  Chord  is  formed  by  raising  the^/f/i  of  the 
Dominant  yth  chord.  This  raised  fifth  sounds  best  when  it  lies  in 
the  upper  voice  and  ought  to  move  a  /lalf  tone  upward. 


t^^^m^^^^^M 


i^l^p^^ 


very  rarely 
used. 


^i^ii^ 


At  f  and  g  two  exceptions  are  introduced  in  which  the  bass-note 
lies  above  the  raised  fifth. 

The  Fourth  Mixed  Chord  is  formed  by  raising  the  seventh  of 
the  Dominant  7th  chord.  From  g,  b,  d,  f,  the  chord  g,  b,  d,  i% 
arises. 

Example  of  Fourth  Mixed  Chord : 


^jfe^^lg^g^lES^i^^EB 


J^l^l^l^l^ 


^i 


7  7e|  I  263 

The  Fifth  Mixed  Chord  is  derived  from  the  Z>?/«/«/^>^^^  Chord 
of  the  Seventh  by  lowering  its  third.  From  g#,  b,  d,  f,  the  chord 
g#,  bb,  d,  f  arises. 


—  45  — 


i=pi|=iil^^l:^^te^l3a=i 


IfT 


The  consecutive  j^//2^  at  c,  are  agreeable  to  the  ear,  and,  hence, 
are  frequently  used ;  they  are  to  be  avoided  only  in  the  outer 
voices.  It  is  advisable  for  the  student  to  practice  w^riting  the  eight 
chords  of  the  Seventh  by  designating  each  by  its  name  or  the  name 
of  the  chord  from  w^hich  it  is  derived,  as  in  the  following  example : 

D  denotes  dominant ;  M,  minor  ;  Dim.,  diminished  ;  and  each  of 
the  mixed  chords  is  marked  I,  II,  III,  etc.  with  Roman  numerals. 


.•_^_ 


^B 


ii, 


5;c 


^=Ei^ 


«  7 

7  V 

D     Dim. 


u 


M       D        i 
III 


2 

IV 


IV     04    7 


Table  of  the  Intervals  of  the  Eight  Chords 
of  the  Seventh, 


Third. 

Fifth. 

Seventh. 

Dominant  Seventh  Chord. 

major. 

major. 

minor. 

Minor  Seventh  Chord. 

minor. 

minor. 

minor. 

Dim.  Seventh  Chord. 

minor. 

minor. 

diminished. 

ist.Mixed  Seventh  Chord. 

minor. 

major. 

minor. 

2d.Mixed  Seventh  Chord. 

major. 

minor. 

minor. 

3d.  Mixed  Seventh  Chord. 

major. 

augmented. 

minor. 

4th. Mixed  Seventh  Chord. 

major. 

major. 

major. 

5th. Mixed  Seventh  Chord. 

diminished. 

minor. 

diminished. 

Further  examples  in  Appendix  Q. 


—  46  — 

If  the  Dominant  Seventh  be  resolved  into  other  tones  than  those 
of  the  tonic,  so-called  deceptive  cadences  are  formed,  which,  how- 
ever, are  employed  only  when  the  Dominant  7th  chord  appears 
without  doubled  bass-note. 

The  most  important  deceptive  cadences  are : 


l^^=s^'=s='=F^=i=i— ^-i='=s=N 


7 7         6  7  6  7       bS  7  4:         6 7         7 


u   etc. 

L  bS  P3  L  L  L  P^ 

6  7    07  7       4      6^6  7      07    bl    bl    bl 


^•^-'-•If  1J»  *  ^if-' •-•^S^If»-^ir^' •-^.— 6i:-" 


The  last  succession  of  Dominant  7th  chords  is  best  treated  in 
the  above  manner;  i.  e.,  by  writing  it  alternately  with  all  its  tones, 
and  then  with  the  fifth  omitted  and  the  bass-tone  doubled  in  its 
place.  Common  tones  are  thus  employed,and  the  chromatic  changes 
are  kept  in  the  same  voices. 

Deceptive  cadences  may  be  used  in  connection  with  the  Inver- 
sions, as  well  as  with  the  original  chords.     For  example  : 


'^^^^i^m^^^^^^Wl^ 


ii^^^^^^^^^^B 


^=s^=Tf^T^T^Frr!^ 


Further  examples  in  Appendix  R. 


—  47  — 

The  chord  of  the  diminished  yth  offers  the  greatest  possibility  of 
modulation  of  all  chords :  from  it,  it  is  possible  to  go  directly  from 
one  key  into  another  and  in  the  following  manner : 

I.  Every  inversion  of  the  diminished  7th  sounds  like  another 
diminished  7th  chord,  and,  by  means  of  enharmonic  changes  can 
be  w^ritten  as  if  it  w^ere  and    resolved  accordingly.     For  example  : 

1 

Into  C.  Into  Et?.  Into  FJf.     •  Into  A. 


2.  The  same  four  modulations  may  be  produced  by  keeping 
three  tones  stationary  and  moving  a  half  tone  dov^nvs^ard  with  one. 
For  example : 

2 

Into  C.  Into  E!7.  Into  FJ$.  Into  A. 

3.  Or  one  tone  may  remain  stationary  and  three  move  a  half 
tone  upward^  and  four  new  keys  be  reached. 

3 

Into  E.  Into  Di?.  Into  G.  Into  Bi?. 


'1^^^y^^^^^}=4^^^'^^^ 


7  be  66 

4.     If  three  tones  move  a  whole  tone  and  one  a  half  tone  up- 
ward^ four  new  keys  may  be  reached. 

4 

Into  F.  Into  D.  Into  Ab.  Into  B  Major. 


bT  ^'    ♦   bf  \%         b7  n  \n    b1  ^  T 


—  48-- 

5-     If  three  tones  move  a  half  tone^  and  one^  a  whole  tone^ 
downward^  four  new  keys  may  also  be  reached. 

5 

Into  F.  Into  D.  Into  At?.  Into  B  Major. 

b7  2  -r  b7  f^  b7       b^3        \'^  b,         «^  I 


6.     The  chord  of  the  diminished  7th  can  be  resolved  into  a  6 
chord  upon  the  degree  a  >^«//*  tone  higher .^  or  a  whole  tone  lower, 

6 

Into  F  Minor.  Into  F  Major.      Into  D  Minor.       Into  D  Major, 


7.     All  the  tones  of  the  diminished  chord  of  the  7th  can  move, 
simultaneously,  a  half  tone  upward  or  downward.     For  example  : 

7  _^ 

Further  examples  of  the  treatment  of  the   diminished  7th  chord 
in  Appendix  S. 


APPENDICES, 


Appendix  A. 

Name  each  of  these  intei*vals,  making  the  major  with  m,  the 
minor  with  min.,  the  diminished  with  dim.,  the  augmented  with 
aug.,  and  the  distance  of  each  interval  by  the  corresponding 
numerals. 

No.   1. 


V^ — 1 

r—'^-'—, — ^^ 

4^-^— 

#      ■   #                 •       '                                    -J 
n 

^-^— 

^  ^-^— ^-8  •  br^-:  V^^-1^=A=^ 

No.  2. 


tr .                                             .  .              II 

(49) 


—  50  — 

Find  the  tones  which,  with  the  tones  given,  will  form  the  inter- 
vals indicated. 


No.  3. 


i^E^ 


w= 


Aug.  5.       min.  7.        m.  7.        dim.  7.      min.  10.      m.  3.         min.  5. 


^=j^— =F-^ — F=g>- 


-^^===g# 


W 


s 


m.  7.  m.  3.        aug.  5.        dim.  3.      aug.  2.      min.  6.      m.  3. 


No.  4. 


Appendix  B. 


i 


j~#" 


s'  «  8 


No.  5. 


^^=E^Er^^^^^E^^^-^=,^^ 


t  0  b  b  b         05    S 


No.  6. 

^ 

^^•tr 

*n.rf    « 

_ 

9 

0 

^    Zi     . 

•     ^ 

• 

«          *        , 

■              « 

0 

I 


«  -•- 


-#-    tf 


No.  7. 


Appendix  C. 


I 


i^i 


No.  8. 


^^^^B 


^^=Ei 


£k 


-• •- 


No.  9. 


©i-^= 


,_^__ 


g 


—  51  — 
Appendix  D. 


No,   10. 


«      f 

No.   11. 


^f 


6 


-^H — -*- 


I 


^ •_ 


-• — • — 


•  '  »• 


No.   12. 


666  60^-6  6  • 

Appendix  E. 


No.   13. 


:9z-fe 


#-•-# 


^-# 


jciiia: 


66*  6  Q  666  66 

No.   14. 


n 


;^^^=?=j=^^^ 


I 


^' 


• — z — a-#- 


^- 


06  Jf60  6666 


MJ^-. 


-f 


No.   15. 


igg^^^^^^ 


6  6  |-#-     tt-JT   §^«-   S-^       — ~^^      

0     S    S     a   ^f       ^•^ 


Appendix  F. 


No.   16.  * 


9i=#: 


I        I  —\-0       *     -^ 


6  6  6 


IB 


^i 


'^^' 


-d • 


*  The  exercises  divided  into  measures  are  to  be  written  in  score ;  i.  e.,  in  all 
the  clefs. 


—  52  — 


No.  17. 


^^^^^^^^^^^m 


%—^ 


Appendix  G. 


No.   18. 


9^ 


;f=^^— «z?^^^=^| 


if-0 


^        ^  "f  -    ®     ®  §  & 

6    5  ^3 


6  6 

4: 


T      li 


No.   19. 


mi^^i^i=i^-^^ 


B 


J       a  J  5     6     a 


£  i 


T    s 


No.  20. 


I     • 


6       6  6       6  5    5 


No.  21 


ms^^^^^^^^^r^ 


^=\ 


t=i: 


-^ ^- 


6  6 


I       «   f 


s 


^^?_ 


r—;i=i 


:i=-tti=^=3F 


6 


r 


-5»-  -^- 


5 


>65 


Appendix  H. 


No.  22. 


m 


^^^^^^m 


'9 9 


? ? ?- 


$  6       6       6       6 

7 


7  7     -— 


No.  23. 


-•-6    5    7  6    6    5  7  6       6  0  6       6       6     -•-  -#-  -•-  ^f-   -#- 


6       6       6     -•-  -•-  -•-  ^:f -   -f- 


53 


No.  24. 


1 1    ^ 


Appendix  I. 


No.  25. 


6       b5  6  6    tj    0    5    5    Q  b5  PS  5     6     0  6     6    -#- 

66  744:366  47 


No.  26. 


11 


t^Jgg: 


"^r"'" 


-• — ^*— • 


5«: 


-*=^=P'=^==^ 


6       5 

6  6 


"f~^ 


No.  27. 


1 


aasfeJ*^ 


«- 


sJ^t 


■s? 


I=#q 


it± 


-(S^        -J-     7     — i- 
6  •  -(5*- 


Appendix  K, 


No.  28. 


^g^J^^P^-^^^^ 


•— • 


3       6 
4 


3  5  05  6       3 

4  6  ^6  4 


,_,__ 


S 


T 


No.  29. 


•-f -?-•-•    6     0    •   -#-   •    te-^—l 5 Ti eT^ 


6  b3 


T 


No.  30. 


—  54  — 
Appendix  L. 


No.  31 


3^ 


:*d2«=i:|,_,_,_,_,_,_*: 


m 


3     6      3  3     6     6     7 

4:  4 


No.  32. 


6      3*     f~6     ?     f   -•- 


.#_•. 


4  «     t     f     5    -§--#-   I     «      2     « 


^^=^E^==H 


6    -»-  6 


No.  33. 


^^^ 


P^=#= 


±3.   ^    F-F-[izE^----^=^-di;jgjz^ 

5  36'        65  3'f'5fi 


«: 


-^^^ 


a 


itit^ITtzl 


tl7         6 


Appendix  M. 


No.  34. 


I 


9^^F*==*^ 


=^^^-b — # 


7  T#-  •     6 #-,6  6 


7  0  7  f  6     5 


b7  4  -^      bs 

7 


No.  35, 


6    0     -#-  •      6       7  jt 

4      #  4  7 


»   ? 


-•—•—•_«_^_lj 


5       JJ  7      0    06       6 


No.  36, 


E§±B: 


-fS f5> «?■ 


t=F 


g^ 


-z:^-. ^- 


e  » 


6  3  6 


r=?^ 


*E 


^9i=fa=t 


t=zl- 


s 


I  ! 


6  ■« 

7 


£      t 


DO 

Appendix  N. 


No.  37. 


:i 


^i 


!=»: 


ZEEi^E?^ 


a_#_#_#_«: 


»  bl  i^i     "11" 


e  be    I    2%   I   •V-ij:'' 


No.  38. 


gi^^Ei^^E^Ei^^^^=^^^l] 


jf    6    5    6    5    6 
o    4    0    4:    4    0 


6       «    -,- 


Appendix  O. 


No.  39. 


s 


:§±^ 


26,6  6  6**  ,2     626-# 


•---# 


7  643  1"'^'^  '^ 


4  7 


No.  40. 


i 


» 


^-, 


-•-•- 


a^ 


•-•— • 


p 


^j— • 


6     0  I     6      2     6b7 

4  7.4: 


6  6 

5  7 


6    ^ 
7 


*T 


No.  41. 


m 


v-l2=li: 


:i2:^=:t=^ 


-fg (^ ^- 


I       i 


=]: 


-^ ^- 


1=2 — ^- 


12^ 


§6  6  6-^  -(5>-. 

4  -s^ 


Appendix  P. 


No.  42. 


azs: 


:#^^^i^p-#i#-*-#: 


1 


^i^fe 


EbE^I^E? 


jT'-*- 


7         g  e  *  a  2  s67   .       6  7     ^7         ^n    '    i   °        °   '' 


«      »  *b« 


—  56  — 


No.  43. 


^^^, 7^ 

'  •  '-•   .        .    II 

^!?    •    1    6 

4     6                    7                    tf       7 

Appendix  Q. 

0 IJ 

t  «  S       ' 

No.  44. 

^ 

3^^^'.^=^ 

^--*J»  •  bEi— Ij 

s    1 1   b^ 


No.  45. 

-m-   6     e      i  6      }      3     6     3     6  bs  -»-        Ox  2     7       6       5     -»- 


'I 


^ 


No.  46. 


^^5i£ggSiisli=fe|||ipB 


07  "7     I     s 


7  4 


b    i  7   -^--ji^  -^- 

5       *  6         " 


Appendix  R. 


No.  47. 


•-* 


^=g»=*-*-g»-^i 


'•-«-• 


765  6  561364:, 6 

4     6  e     4:\,j     4     2bs 


-#_#. 


9 


b7     6      4      3 


No.  48. 


^>-.  ^  ;^ — = — —     — =F| 

-       '    •~wz:m^_^      _^_0_0^    m4p  • w-=W 

2446       56       7. «6f. 4:      6       2^    D7       5  -f-   7    --- 


m*=i 


^  I  i  I   I  I   '  Bi  M  of 

a      « 


No.  49. 


^^ 


iz^irpc 


a3^=F=t 


3^^^^^ 


«   i   I 


fei 


7     qD^  05 


P9i!3EEES 


d=: 


■«-=!■ 


■i    i     ?-•    ^t<-;-'- 


I5 


-s)-' 


^— 


9 


Appendix  S. 


No.  50. 


'--       ^  b7       3       6     5         b7     2   bs   be   b?  e     7 


b7 
No.  51 


fi^E^^^ 


m] 


J7     0     e  ^  ^7  ff*  5*    -#-  -#- 


0     6   b7   be   ,  f  n-t     6   ,  6   be   b7     0     e  ♦'r  '^  5*  9^*    -#-  -#- 
4  4  b5     2         bs     4  54  0     0     e     * 

3  5     5     4     * 

7 

No.  52.  

^^^^r        .  L__J '  n'7h«      •>       «  hikaflfihR      rr  a      ?»      ', 


_  b7  Qe    2     6        bs  bs  Q3   Qe    7 

g     6       b:i      5  J  b7  04  b7       -* 

7  Qe 


V 


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